Here's why this works:
* Palter means to act in a shifty or evasive way, especially to avoid telling the truth.
* The sentence implies the politician is being dishonest and trying to mislead the reporter.
Here are some other ways to use "palter":
* "She paltered with her friends, pretending she was busy when she just wanted to stay home and read." (Meaning: she gave a false excuse)
* "The company paltered with the facts, making their product seem safer than it really was." (Meaning: they lied or distorted the truth)
Important note: "Palter" is often used in a negative way, implying deceitfulness.